← Find the total first, then divide · Division as the Inverse of Multiplication

Find the total first, then divide · 10 practice problems

3.OA.D.83.OA.A.3

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Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy

Some crayons were packed equally, $6$ to a bag, making $6$ bags. If these same crayons are repacked equally into $4$ bags, how many crayons can be put in each bag?

Your answer

Show solution

1 · Understandwhat's really being asked

Crayons were packed 6 to a bag into 6 bags. The same crayons are then repacked equally into 4 bags. I need to find how many go in each of the new bags.

Givens

Each original bag holds 6 crayons.
There are 6 original bags.
All the crayons are repacked equally into 4 bags.

Unknowns

The number of crayons in each of the 4 new bags.

Constraints

The crayons are split equally with none left over.
The total number stays the same when repacked.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

This is a two-step calculation: first find the total (a multiplication subproblem), then split that total equally into the new bags (a division subproblem). Watching the units keeps the setup honest.

3 · Execute2 carry out the plan

1Find the total number of crayons

#7 Identify Subproblems 3.OA.A.3

There are 6 bags with 6 crayons each, so multiply to find how many crayons there are altogether.

6 \times 6 = 36

Equal groups are counted by multiplying the group size by the number of groups.

2Split the total equally into 4 bags

#8 Analyze the Units 3.OA.A.3

The same 36 crayons are repacked equally into 4 bags, so divide the total by the number of new bags.

36 \div 4 = 9

Sharing a total equally into a known number of groups is exactly what division finds.

Answer: 9 crayons

4 · Reviewdoes it hold up?

Check: 9 crayons per bag times 4 bags equals 36, the same total we started with.

Another way: Look for a pattern (tool 5): the total 36 shared into 4 equal bags gives 9 per bag.

Standardsmin grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying to get the total, then dividing the total equally among the new bags.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Combining the multiply-then-divide steps into one two-step word problem.

💡Takeaway. Find the whole pile first, then share it out: that's all this Grade 3 problem needs!

Variant 2 easy

Some marbles were packed equally, $8$ to a bag, making $6$ bags. If these same marbles are repacked equally into $4$ bags, how many marbles can be put in each bag?

Your answer

Show solution

1 · Understandwhat's really being asked

Marbles were packed 8 to a bag into 6 bags. The same marbles are then repacked equally into 4 bags. I need to find how many go in each of the new bags.

Givens

Each original bag holds 8 marbles.
There are 6 original bags.
All the marbles are repacked equally into 4 bags.

Unknowns

The number of marbles in each of the 4 new bags.

Constraints

The marbles are split equally with none left over.
The total number stays the same when repacked.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

This is a two-step calculation: first find the total (a multiplication subproblem), then split that total equally into the new bags (a division subproblem). Watching the units keeps the setup honest.

3 · Execute2 carry out the plan

1Find the total number of marbles

#7 Identify Subproblems 3.OA.A.3

There are 6 bags with 8 marbles each, so multiply to find how many marbles there are altogether.

8 \times 6 = 48

Equal groups are counted by multiplying the group size by the number of groups.

2Split the total equally into 4 bags

#8 Analyze the Units 3.OA.A.3

The same 48 marbles are repacked equally into 4 bags, so divide the total by the number of new bags.

48 \div 4 = 12

Sharing a total equally into a known number of groups is exactly what division finds.

Answer: 12 marbles

4 · Reviewdoes it hold up?

Check: 12 marbles per bag times 4 bags equals 48, the same total we started with.

Another way: Look for a pattern (tool 5): the total 48 shared into 4 equal bags gives 12 per bag.

Standardsmin grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying to get the total, then dividing the total equally among the new bags.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Combining the multiply-then-divide steps into one two-step word problem.

💡Takeaway. Find the whole pile first, then share it out: that's all this Grade 3 problem needs!

Variant 3 easy

Some candies were packed equally, $9$ to a bag, making $8$ bags. If these same candies are repacked equally into $6$ bags, how many candies can be put in each bag?

Your answer

Show solution

1 · Understandwhat's really being asked

Candies were packed 9 to a bag into 8 bags. The same candies are then repacked equally into 6 bags. I need to find how many go in each of the new bags.

Givens

Each original bag holds 9 candies.
There are 8 original bags.
All the candies are repacked equally into 6 bags.

Unknowns

The number of candies in each of the 6 new bags.

Constraints

The candies are split equally with none left over.
The total number stays the same when repacked.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

This is a two-step calculation: first find the total (a multiplication subproblem), then split that total equally into the new bags (a division subproblem). Watching the units keeps the setup honest.

3 · Execute2 carry out the plan

1Find the total number of candies

#7 Identify Subproblems 3.OA.A.3

There are 8 bags with 9 candies each, so multiply to find how many candies there are altogether.

9 \times 8 = 72

Equal groups are counted by multiplying the group size by the number of groups.

2Split the total equally into 6 bags

#8 Analyze the Units 3.OA.A.3

The same 72 candies are repacked equally into 6 bags, so divide the total by the number of new bags.

72 \div 6 = 12

Sharing a total equally into a known number of groups is exactly what division finds.

Answer: 12 candies

4 · Reviewdoes it hold up?

Check: 12 candies per bag times 6 bags equals 72, the same total we started with.

Another way: Look for a pattern (tool 5): the total 72 shared into 6 equal bags gives 12 per bag.

Standardsmin grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying to get the total, then dividing the total equally among the new bags.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Combining the multiply-then-divide steps into one two-step word problem.

💡Takeaway. Find the whole pile first, then share it out: that's all this Grade 3 problem needs!

Variant 4 medium

Some apples were packed equally, $10$ to a bag, making $4$ bags. If these same apples are repacked equally into $5$ bags, how many apples can be put in each bag?

Your answer

Show solution

1 · Understandwhat's really being asked

Apples were packed 10 to a bag into 4 bags. The same apples are then repacked equally into 5 bags. I need to find how many go in each of the new bags.

Givens

Each original bag holds 10 apples.
There are 4 original bags.
All the apples are repacked equally into 5 bags.

Unknowns

The number of apples in each of the 5 new bags.

Constraints

The apples are split equally with none left over.
The total number stays the same when repacked.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

This is a two-step calculation: first find the total (a multiplication subproblem), then split that total equally into the new bags (a division subproblem). Watching the units keeps the setup honest.

3 · Execute2 carry out the plan

1Find the total number of apples

#7 Identify Subproblems 3.OA.A.3

There are 4 bags with 10 apples each, so multiply to find how many apples there are altogether.

10 \times 4 = 40

Equal groups are counted by multiplying the group size by the number of groups.

2Split the total equally into 5 bags

#8 Analyze the Units 3.OA.A.3

The same 40 apples are repacked equally into 5 bags, so divide the total by the number of new bags.

40 \div 5 = 8

Sharing a total equally into a known number of groups is exactly what division finds.

Answer: 8 apples

4 · Reviewdoes it hold up?

Check: 8 apples per bag times 5 bags equals 40, the same total we started with.

Another way: Look for a pattern (tool 5): the total 40 shared into 5 equal bags gives 8 per bag.

Standardsmin grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying to get the total, then dividing the total equally among the new bags.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Combining the multiply-then-divide steps into one two-step word problem.

💡Takeaway. Find the whole pile first, then share it out: that's all this Grade 3 problem needs!

Variant 5 medium

Some tangerines were packed equally, $12$ to a bag, making $3$ bags. If these same tangerines are repacked equally into $6$ bags, how many tangerines can be put in each bag?

Your answer

Show solution

1 · Understandwhat's really being asked

Tangerines were packed 12 to a bag into 3 bags. The same tangerines are then repacked equally into 6 bags. I need to find how many go in each of the new bags.

Givens

Each original bag holds 12 tangerines.
There are 3 original bags.
All the tangerines are repacked equally into 6 bags.

Unknowns

The number of tangerines in each of the 6 new bags.

Constraints

The tangerines are split equally with none left over.
The total number stays the same when repacked.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

This is a two-step calculation: first find the total (a multiplication subproblem), then split that total equally into the new bags (a division subproblem). Watching the units keeps the setup honest.

3 · Execute2 carry out the plan

1Find the total number of tangerines

#7 Identify Subproblems 3.OA.A.3

There are 3 bags with 12 tangerines each, so multiply to find how many tangerines there are altogether.

12 \times 3 = 36

Equal groups are counted by multiplying the group size by the number of groups.

2Split the total equally into 6 bags

#8 Analyze the Units 3.OA.A.3

The same 36 tangerines are repacked equally into 6 bags, so divide the total by the number of new bags.

36 \div 6 = 6

Sharing a total equally into a known number of groups is exactly what division finds.

Answer: 6 tangerines

4 · Reviewdoes it hold up?

Check: 6 tangerines per bag times 6 bags equals 36, the same total we started with.

Another way: Look for a pattern (tool 5): multiplying the number of bags by 2 divides the count per bag by 2: 12 becomes 6 without computing the total at all.

Standardsmin grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying to get the total, then dividing the total equally among the new bags.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Combining the multiply-then-divide steps into one two-step word problem.

💡Takeaway. Find the whole pile first, then share it out: that's all this Grade 3 problem needs!

Variant 6 medium

Some buttons were packed equally, $12$ to a bag, making $5$ bags. If these same buttons are repacked equally into $4$ bags, how many buttons can be put in each bag?

Your answer

Show solution

1 · Understandwhat's really being asked

Buttons were packed 12 to a bag into 5 bags. The same buttons are then repacked equally into 4 bags. I need to find how many go in each of the new bags.

Givens

Each original bag holds 12 buttons.
There are 5 original bags.
All the buttons are repacked equally into 4 bags.

Unknowns

The number of buttons in each of the 4 new bags.

Constraints

The buttons are split equally with none left over.
The total number stays the same when repacked.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

This is a two-step calculation: first find the total (a multiplication subproblem), then split that total equally into the new bags (a division subproblem). Watching the units keeps the setup honest.

3 · Execute2 carry out the plan

1Find the total number of buttons

#7 Identify Subproblems 3.OA.A.3

There are 5 bags with 12 buttons each, so multiply to find how many buttons there are altogether.

12 \times 5 = 60

Equal groups are counted by multiplying the group size by the number of groups.

2Split the total equally into 4 bags

#8 Analyze the Units 3.OA.A.3

The same 60 buttons are repacked equally into 4 bags, so divide the total by the number of new bags.

60 \div 4 = 15

Sharing a total equally into a known number of groups is exactly what division finds.

Answer: 15 buttons

4 · Reviewdoes it hold up?

Check: 15 buttons per bag times 4 bags equals 60, the same total we started with.

Another way: Look for a pattern (tool 5): the total 60 shared into 4 equal bags gives 15 per bag.

Standardsmin grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying to get the total, then dividing the total equally among the new bags.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Combining the multiply-then-divide steps into one two-step word problem.

💡Takeaway. Find the whole pile first, then share it out: that's all this Grade 3 problem needs!

Variant 7 medium

Some cookies were packed equally, $14$ to a bag, making $2$ bags. If these same cookies are repacked equally into $4$ bags, how many cookies can be put in each bag?

Your answer

Show solution

1 · Understandwhat's really being asked

Cookies were packed 14 to a bag into 2 bags. The same cookies are then repacked equally into 4 bags. I need to find how many go in each of the new bags.

Givens

Each original bag holds 14 cookies.
There are 2 original bags.
All the cookies are repacked equally into 4 bags.

Unknowns

The number of cookies in each of the 4 new bags.

Constraints

The cookies are split equally with none left over.
The total number stays the same when repacked.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

This is a two-step calculation: first find the total (a multiplication subproblem), then split that total equally into the new bags (a division subproblem). Watching the units keeps the setup honest.

3 · Execute2 carry out the plan

1Find the total number of cookies

#7 Identify Subproblems 3.OA.A.3

There are 2 bags with 14 cookies each, so multiply to find how many cookies there are altogether.

14 \times 2 = 28

Equal groups are counted by multiplying the group size by the number of groups.

2Split the total equally into 4 bags

#8 Analyze the Units 3.OA.A.3

The same 28 cookies are repacked equally into 4 bags, so divide the total by the number of new bags.

28 \div 4 = 7

Sharing a total equally into a known number of groups is exactly what division finds.

Answer: 7 cookies

4 · Reviewdoes it hold up?

Check: 7 cookies per bag times 4 bags equals 28, the same total we started with.

Another way: Look for a pattern (tool 5): multiplying the number of bags by 2 divides the count per bag by 2: 14 becomes 7 without computing the total at all.

Standardsmin grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying to get the total, then dividing the total equally among the new bags.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Combining the multiply-then-divide steps into one two-step word problem.

💡Takeaway. Find the whole pile first, then share it out: that's all this Grade 3 problem needs!

Variant 8 hard

Some stickers were packed equally, $15$ to a bag, making $4$ bags. If these same stickers are repacked equally into $6$ bags, how many stickers can be put in each bag?

Your answer

Show solution

1 · Understandwhat's really being asked

Stickers were packed 15 to a bag into 4 bags. The same stickers are then repacked equally into 6 bags. I need to find how many go in each of the new bags.

Givens

Each original bag holds 15 stickers.
There are 4 original bags.
All the stickers are repacked equally into 6 bags.

Unknowns

The number of stickers in each of the 6 new bags.

Constraints

The stickers are split equally with none left over.
The total number stays the same when repacked.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

This is a two-step calculation: first find the total (a multiplication subproblem), then split that total equally into the new bags (a division subproblem). Watching the units keeps the setup honest.

3 · Execute2 carry out the plan

1Find the total number of stickers

#7 Identify Subproblems 3.OA.A.3

There are 4 bags with 15 stickers each, so multiply to find how many stickers there are altogether.

15 \times 4 = 60

Equal groups are counted by multiplying the group size by the number of groups.

2Split the total equally into 6 bags

#8 Analyze the Units 3.OA.A.3

The same 60 stickers are repacked equally into 6 bags, so divide the total by the number of new bags.

60 \div 6 = 10

Sharing a total equally into a known number of groups is exactly what division finds.

Answer: 10 stickers

4 · Reviewdoes it hold up?

Check: 10 stickers per bag times 6 bags equals 60, the same total we started with.

Another way: Look for a pattern (tool 5): the total 60 shared into 6 equal bags gives 10 per bag.

Standardsmin grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying to get the total, then dividing the total equally among the new bags.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Combining the multiply-then-divide steps into one two-step word problem.

💡Takeaway. Find the whole pile first, then share it out: that's all this Grade 3 problem needs!

Variant 9 hard

Some pencils were packed equally, $18$ to a bag, making $2$ bags. If these same pencils are repacked equally into $9$ bags, how many pencils can be put in each bag?

Your answer

Show solution

1 · Understandwhat's really being asked

Pencils were packed 18 to a bag into 2 bags. The same pencils are then repacked equally into 9 bags. I need to find how many go in each of the new bags.

Givens

Each original bag holds 18 pencils.
There are 2 original bags.
All the pencils are repacked equally into 9 bags.

Unknowns

The number of pencils in each of the 9 new bags.

Constraints

The pencils are split equally with none left over.
The total number stays the same when repacked.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

This is a two-step calculation: first find the total (a multiplication subproblem), then split that total equally into the new bags (a division subproblem). Watching the units keeps the setup honest.

3 · Execute2 carry out the plan

1Find the total number of pencils

#7 Identify Subproblems 3.OA.A.3

There are 2 bags with 18 pencils each, so multiply to find how many pencils there are altogether.

18 \times 2 = 36

Equal groups are counted by multiplying the group size by the number of groups.

2Split the total equally into 9 bags

#8 Analyze the Units 3.OA.A.3

The same 36 pencils are repacked equally into 9 bags, so divide the total by the number of new bags.

36 \div 9 = 4

Sharing a total equally into a known number of groups is exactly what division finds.

Answer: 4 pencils

4 · Reviewdoes it hold up?

Check: 4 pencils per bag times 9 bags equals 36, the same total we started with.

Another way: Look for a pattern (tool 5): the total 36 shared into 9 equal bags gives 4 per bag.

Standardsmin grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying to get the total, then dividing the total equally among the new bags.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Combining the multiply-then-divide steps into one two-step word problem.

💡Takeaway. Find the whole pile first, then share it out: that's all this Grade 3 problem needs!

Variant 10 hard

Some beads were packed equally, $20$ to a bag, making $3$ bags. If these same beads are repacked equally into $5$ bags, how many beads can be put in each bag?

Your answer

Show solution

1 · Understandwhat's really being asked

Beads were packed 20 to a bag into 3 bags. The same beads are then repacked equally into 5 bags. I need to find how many go in each of the new bags.

Givens

Each original bag holds 20 beads.
There are 3 original bags.
All the beads are repacked equally into 5 bags.

Unknowns

The number of beads in each of the 5 new bags.

Constraints

The beads are split equally with none left over.
The total number stays the same when repacked.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

This is a two-step calculation: first find the total (a multiplication subproblem), then split that total equally into the new bags (a division subproblem). Watching the units keeps the setup honest.

3 · Execute2 carry out the plan

1Find the total number of beads

#7 Identify Subproblems 3.OA.A.3

There are 3 bags with 20 beads each, so multiply to find how many beads there are altogether.

20 \times 3 = 60

Equal groups are counted by multiplying the group size by the number of groups.

2Split the total equally into 5 bags

#8 Analyze the Units 3.OA.A.3

The same 60 beads are repacked equally into 5 bags, so divide the total by the number of new bags.

60 \div 5 = 12

Sharing a total equally into a known number of groups is exactly what division finds.

Answer: 12 beads

4 · Reviewdoes it hold up?

Check: 12 beads per bag times 5 bags equals 60, the same total we started with.

Another way: Look for a pattern (tool 5): the total 60 shared into 5 equal bags gives 12 per bag.

Standardsmin grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying to get the total, then dividing the total equally among the new bags.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Combining the multiply-then-divide steps into one two-step word problem.

💡Takeaway. Find the whole pile first, then share it out: that's all this Grade 3 problem needs!

Where next?

← Back to the problem: Find the total first, then divide